Abstract
In this investigation the attention is given to a mathematical model of the non-Newtonian Casson liquid over an unsteady stretching sheet under the combined effects of different natural parameters with heat transfer in the presence of suction/injection phenomena. The movement of a laminar thin liquid film and associated heat transfer from a horizontal stretching surface is studied. Magnetic field is proposed perpendicular to the direction of flow, while surface tension is varied quadratically with temperature of the conducting fluid. Further, variable viscosity and thermal conductivity (linear function of temperature) of the flow are examined. The transformation allows to convert the boundary layer model to a system of nonlinear ODEs (ordinary differential equations). Analytical and numerical solutions of the resulting nonlinear ODEs are obtained by using HAM and BVP4C package. Thickness of the boundary layer is investigated by both methods for a classical selection of the unsteadiness parameter. A selection of the parameter ranges is studied for better solution of the problem. Present observation displays the joined effects of magnetic field, surface tension, suction/injection, and slippage at the boundary is to improve the thermal boundary layer thickness. Results for the heat flux (Nusselt number), skin friction coefficient, and free surface temperature are granted graphically and in a table form. Similarly, the effects of natural parameters on the velocity and temperature profiles are investigated.
Highlights
A large number of industrial processes, the effect of boundary layer flow with heat transfer over an unsteady stretching sheet with free surface flow have wide use in wire coating, drawing of plastic sheets, metal and polymer extrusion, foodstuff processing, daily life uses equipments, etc
3.3 Results and discussion The modeled problem consists of a couple of ODEs shown in Eqs. (24) and (25) with the defined physically admitted boundary conditions mentioned in (26) and (27)
They are solved by the well-known methods called HAM and shooting method for arbitrary values of the interesting non-dimensional parameters listed as Grashof number, unsteady parameter, skin friction, thermal conductivity parameter, heat flux, Hartmann parameter, variable viscosity parameter, film thickness, free surface temperature, suction/injection parameter, Prandtl number, Casson parameter, slip velocity parameter, and thermocapillary number
Summary
A large number of industrial processes, the effect of boundary layer flow with heat transfer over an unsteady stretching sheet with free surface flow have wide use in wire coating, drawing of plastic sheets, metal and polymer extrusion, foodstuff processing, daily life uses equipments, etc.
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